GENERAL I ARTICLE Opinion Polls and Statistical Surveys: What They Really Tell Us Rajeeva L Karandikar and Ayanendranath Basil In recent times we seem to be having frequent parliamen­ tary elections in addition to lots of assembly elections. Even as this article is being written, we are heading for another parliamentary election. At the same time, exit polls and opinion polls are gaining popularity. The media often re­ ports the results of opinion polls predicti~g the seat shares of major parties before the actual elections; even exit polls Ayanendranath Basa is with are now commonplace. All major national and state elec­ the Indian Statistical tions in the recent times have been covered by exit polls. Iastihte, Calcatta. He The agencies conducting these polls now recruit the services received the MStat. desree from the Indian Statistical of highly qualified experts for this purpose. Iastihte in 1986 and the At the same time, however, the general public of our coun­ PhD desree from Peaasylvania State try are largely unaware of the scientific issues involved in University, USA in 1991. a statistically planned opinion survey (or sometimes 'even After spendias foar years at what it means). This leads to fantastic claims ~d counter­ the University of Texas, he claims from politicians (depending on whether their parties rehraed to the Indian Statistical Iastihte in 1995. are projected to win or lose); some statements go as far as His research interests asserting that opinion polls mean nothing and there is no indade robast estimation, science behind them. While the analysis of exit polls at shape estimation, and DIV the Doordarshan Channel was going on after the 1998 par­ l;Ilodellins· liamentary elections, an otherwise respected political leader claimed that any opinion based on a sample of size 26900 in a country of 26 crore voters cannot give any meaningful information. I t is true that no survey, not even the most optimally designed one, can predict the true state of nature with complete confidence, and there is always a degree of uncertainty involved. However, when the confusion reaches Rajeeva Karandikar is with such a stage where a layman freely questions the findings of a the Indian Statistical scientific study, it becomes the duty of the scientific commu­ Instihte, New Delhi. De received his PhD from the nity to.justify the merits and scope of such techniques. Can Indian Statistical Institute a sample of 26000 really lead to any meaningful conclusions in 1982. His research in a country so large and diverse as India? interests incl.de stochastic processes and f'dterins The first step in an exit/opinion poll (or for that matter theory. ----------------~----------------RESONANCE I July 1999 49 GENERAL I ARTICLE When confusion any other statistical survey) is the estimation of some un­ reaches such a known parameter. (See Delampady & Padmawar, Reso­ nance, Vol. 1, No.5 for some simple examples on parameter stage where a estimation.) While in the context of elections one can con­ layman freely sider the unknown parameter to be the proportion of voters questions the who intend to vote for a particular party (or alliance), indeed findings of a this is also the case for other social or economic parameters scientific study I it such as literacy ratios, unemployment rates, proportion of becomes the duty people below the poverty line, proportion of vehicle, house, of the scientific TV and telephone connection owners and many such other community to things. If we were to simply estimate a population propor­ justify the merits tion (the proportion of votes for a given party in the election context), it can be done fairly accurately based on the in­ and scope of such formation of a subset of the population - called the sample, techniques. provided the sample was large enough and 'properly' chosen (discussed in detail later). In an election, however, the main interest of the populace (and hence the media) is not in the percentage of votes for a given party (or alliance), but rather in its seat share. This makes the problem complicated, and we need further analysis than the simple statistical estima­ tion of a population proportion. If the entire population size is small, we can probably enu­ merate all the individuals and thereby determine the exact proportion of individuals of each different type making up the population. Often, however, the population of interest will be so big that complete enumeration will be totally im­ practical - perhaps even impossible - due to constraints on essential resources such as money, time, manpower, etc. It is in situations such as this that the idea of a statistical survey becomes relevant. In these cases, statisticians must base their estimate of the unknown proportion on a smaller fraction of the actual population - the so called sample. In the context of the parliamentary election, if one wants to predict the winner in each constituency of Lok Sabha with a high degree of confidence, one has to sample a reason­ ably large number, say 500, of individuals from each of our 544 constituencies. This will make the overall sample size prohibitively large, and the entire process will become an unmanageable and time-consuming exercise even if one had -50-----------------------------~--------------R-ES-O-N-A-N-C-E-\-J-U-IY--l-9--99 GENERAL I ARTICLE adequate financial resources. I t becomes necessary there­ fore to restrict attention to a set of selected constituencies in some optimum way. The data obtained by sampling from these constituencies is then combined with some other infor­ mation such as past voting trends and records, and the seat shares are then predicted based on a suitable mathematical model. Since we get the actual information only from a subset of the total number of constituencies, the selection of the con­ stituencies to be sampled is of great importance. In the United Kingdom, where the procedures for general elections and installation of new governments are very similar to our system, the idea of 'safe seats' is often used in the deter­ mination of the constituencies to be sampled. Both the Conservative and the Labour parties have large committed vote banks; voting patterns in UK change slowly, so that the constituencies with overwhelming support for one of the two parties can often be considered safe for the given party at elections in the not too distant future. For prediction purposes, one can therefore concentrate on the remaining marginal seats. In India, the situation is quite different. Our election pro­ cess involves a very large number of national and regional parties. Politics in India is largely personality-based rather than issue-based. Voter moods appear to be more easily swayed here, The political parties keep splitting and re­ grouping in different fonnations; old alliances are broken up and new alliances are created. All this causes voter loyalties to shift often and by wide margins, and there are very few safe seats. In addition, major events which have large im­ pacts on voter's perception often have a very regional nature in a diverse country like India. All these make the use of the safe seat idea a rather shaky one in the Indian context. We now discuss one by one the two stages of estimating the seat share of a particular party; these are (i) estimating the proportion of votes for a given party in a given region and (ii) estimating the corresponding number of seats based on a suitable model. -RE-S-O-N-A-N-C-E-I-J-UI-Y--19-9-9-------------~------------------------------51 GENERAL I ARTICLE As the statistician This problem may also be described in terms of urns and will not have balls - as there being an urn with a very large number of complete balls of k different colours, and we have to draw a sample of information about appropriate size to eStimate the actual proportion of balls of each colour in the urn. As the statistician will not have com­ the population, it is plete information about the population, it is improbable that improbable that the estimate offered on the basis of the sample observations the estimate (whatever it may be, usually it is the observed proportion offered on the based on the sample) will actually be exactly equal to the basis of the desired target - unless that happens to be a lucky coinci­ sample dence. Allowing for a margin of error, one must therefore observations will try to minimize the error in some average sense. One of the actually be exactly keys to this generally lies in the technique that is employed equal to the in choosing the sample on which the statistician's inference is to be based - it must be 'representative' of the pattern desired target. of the true population. In the simplest case this is done through 'simple random sampling' (equal probability sam­ pling) where one chooses a sample of a given size from the population in such a way that each individual in the popu­ lation has the same chance of being included in the sample. This is necessary to diminish the possibility of the sample drawn being biased in the sense of being concentrated on a particular segment of the entire population. This random­ ness is a property of the sample collection method and not of the actual sample. It is not possible to say just by look­ ing at the sample whether the particular sample has been chosen randomly or through some systematic procedure. In fact even the random sampling procedure may occasionally result in a biased sample, the conclusions based on which may be far off from the truth; however the randomness of the procedure ensures that this is unlikely.